Eighteen people contributed to a certain charity. There were six contributions of $\$ 10$, six of $\$ 20$, and six of $\$ 30$. What is the mean value of the contributions?
Solution: We find that $\frac{1}{18} \cdot (6\cdot 10 + 6 \cdot 20 + 6 \cdot 30) = \frac{1}{18}\cdot 6 \cdot (10 + 20 + 30) = \frac{1}{3}\cdot 60 = \boxed{20}$ dollars. Alternatively, we can see that the contributions are "centered" at $\$20$: the contributions below $\$20$ are just as many as the contributions above $\$20$ and are just as far below $\$20$ as the contributions above $\$20$ are above.